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Documents authored by Mousavi, Ramin

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APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.13
A Constant-Factor Approximation for Quasi-Bipartite Directed Steiner Tree on Minor-Free Graphs

Authors: Zachary Friggstad and Ramin Mousavi

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We give the first constant-factor approximation algorithm for quasi-bipartite instances of Directed Steiner Tree on graphs that exclude fixed minors. In particular, for K_r-minor-free graphs our approximation guarantee is O(r⋅√(log r)) and, further, for planar graphs our approximation guarantee is 20. Our algorithm uses the primal-dual scheme. We employ a more involved method of determining when to buy an edge while raising dual variables since, as we show, the natural primal-dual scheme fails to raise enough dual value to pay for the purchased solution. As a consequence, we also demonstrate integrality gap upper bounds on the standard cut-based linear programming relaxation for the Directed Steiner Tree instances we consider.
Cite as

Zachary Friggstad and Ramin Mousavi. A Constant-Factor Approximation for Quasi-Bipartite Directed Steiner Tree on Minor-Free Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{friggstad_et_al:LIPIcs.APPROX/RANDOM.2023.13,
  author =	{Friggstad, Zachary and Mousavi, Ramin},
  title =	{{A Constant-Factor Approximation for Quasi-Bipartite Directed Steiner Tree on Minor-Free Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.13},
  URN =		{urn:nbn:de:0030-drops-188389},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.13},
  annote =	{Keywords: Directed Steiner tree, Combinatorial optimization, approximation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.63
An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs

Authors: Zachary Friggstad and Ramin Mousavi

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We present an O(log k)-approximation for both the edge-weighted and node-weighted versions of Directed Steiner Tree in planar graphs where k is the number of terminals. We extend our approach to Multi-Rooted Directed Steiner Tree, in which we get a O(R+log k)-approximation for planar graphs for where R is the number of roots.
Cite as

Zachary Friggstad and Ramin Mousavi. An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{friggstad_et_al:LIPIcs.ICALP.2023.63,
  author =	{Friggstad, Zachary and Mousavi, Ramin},
  title =	{{An O(log k)-Approximation for Directed Steiner Tree in Planar Graphs}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.63},
  URN =		{urn:nbn:de:0030-drops-181156},
  doi =		{10.4230/LIPIcs.ICALP.2023.63},
  annote =	{Keywords: Directed Steiner tree, Combinatorial optimization, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.8
Bi-Criteria Approximation Algorithms for Bounded-Degree Subset TSP

Authors: Zachary Friggstad and Ramin Mousavi

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We initiate the study of the Bounded-Degree Subset Traveling Salesman problem (BDSTSP) in which we are given a graph G = (V,E) with edge cost c_e ≥ 0 on each edge e, degree bounds b_v ≥ 0 on each vertex v ∈ V and a subset of terminals X ⊆ V. The goal is to find a minimum-cost closed walk that spans all terminals and visits each vertex v ∈ V at most b_v/2 times. In this paper, we study bi-criteria approximations that find tours whose cost is within a constant-factor of the optimum tour length while violating the bounds b_v at each vertex by additive quantities. If X = V, an adaptation of the Christofides-Serdyukov algorithm yields a (3/2, +4)-approximation, that is the tour passes through each vertex at most b_v/2+2 times (the degree of v in the multiset of edges on the tour being at most b_v + 4). This is enabled through known results in bounded-degree Steiner trees and integrality of the bounded-degree Y-join polytope. The general case X ≠ V is more challenging since we cannot pass to the metric completion on X. However, it is at least simple to get a (5/3, +4)-bicriteria approximation by using ideas similar to Hoogeveen’s TSP-Path algorithm. Our main result is an improved approximation with marginally worse violations of the vertex bounds: a (13/8, +6)-approximation. We obtain this primarily through adapting the bounded-degree Steiner tree approximation to ensure certain "dangerous" nodes always have even degree in the resulting tree which allows us to bound the cost of the resulting degree-bounded Y-join. We also recover a (3/2, +8)-approximation for this general case.
Cite as

Zachary Friggstad and Ramin Mousavi. Bi-Criteria Approximation Algorithms for Bounded-Degree Subset TSP. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{friggstad_et_al:LIPIcs.ISAAC.2022.8,
  author =	{Friggstad, Zachary and Mousavi, Ramin},
  title =	{{Bi-Criteria Approximation Algorithms for Bounded-Degree Subset TSP}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.8},
  URN =		{urn:nbn:de:0030-drops-172932},
  doi =		{10.4230/LIPIcs.ISAAC.2022.8},
  annote =	{Keywords: Linear programming, approximation algorithms, combinatorial optimization}
}
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